What would the percentage of thorium-232 (parent compound) be in a rock that was dated at 2.8 billions years?

The half-life of Th-232 is 1.405 × 10¹⁰ years  

Time elapsed = 2.8 x 10⁹ years  

Equation of radioactive decay:

A = A₀ = (1/2)^ t/t₁/₂

where A₀ is the initial amount, A is the amount after time t, t₁/₂ is the half file

The fraction of thorium-232 that remains in the rock after 2.8 billions years is,

A/A₀ = (1/2) ^ (2.8 x 10⁹/ 1.405 × 10¹⁰) = 0.871

Therefore, the percentage of thorium-232 in the rock that was dated at 2.8 billions year = 87.1%

a rain shadow is a dry region of land on the side that is protected against the prevailing winds of a mountain range. the prevailing winds are the winds that occur most of the time in a particular place of the earth

prevailing winds carry air toward the mountain range. as the air rises up over a mountain range, the air cools, water vapor condenses, and clouds form. on this side of the mountains, called the windward side, precipitation falls in the form of  rain  or snow. this dry air produces a  rain shadow.

answer: semi-infinite solid initially at a uniform temperature of 400 ◦c is cooled at its surface by convection. the cooling fluid at a constant temperature of 200 ◦c has a convective coefficient (ha) of 250 w/m2.k. the physical properties of the solid: k = 20 w/m.k and α = 4 * 10-5  m2/s. using δx = 0.04 m and δt = 10 s. write the finite difference equations describing the transient heat transfer of the first five δx and the temperature profile after 30 s.